Precise radial velocities of giant stars. XI. Two brown dwarfs in 6:1 mean motion resonance around the K giant star $\nu$ Ophiuchi

We present radial-velocity (RV) measurements for the K giant $\nu$ Oph (= HIP88048, HD163917, HR6698), which reveal two brown dwarf companions with a period ratio close to 6:1. For our orbital analysis we use 150 precise RV measurements taken at Lick Observatory between 2000 and 2011, and we combine them with RV data for this star available in the literature. Using a stellar mass of $M=2.7M_{\odot }$ for $\nu$ Oph and applying a self-consistent N-body model we estimate the minimum dynamical companion masses to be $m_1\sin i \approx 22.2,M_{$\mathrm{J}\mathrm{u}\mathrm{p}$}$and$m_2\sin i \approx 24.7,M_{$\mathrm{J}\mathrm{u}\mathrm{p}$}$, with orbital periods $P_1\approx 530$ d and $P_2\approx 3185$ d. We study a large set of potential orbital configurations for this system, employing a bootstrap analysis and a systematic ${\chi }_{\nu }^2$ grid-search coupled with our dynamical fitting model, and we examine their long-term stability. We find that the system is indeed locked in a 6:1 mean motion resonance (MMR), with $\Delta \omega$andallsixresonanceangles$\theta_{1}, \ldots, \theta_{6}$ librating around 0${}^{\circ }$. We also test a large set of coplanar inclined configurations, and we find that the system will remain in a stable resonance for most of these configurations. The $\nu$ Oph system is important for probing planetary formation and evolution scenarios. It seems very likely that the two brown dwarf companions of $\nu$ Oph formed like planets in a circumstellar disk around the star and have been trapped in a MMR by smooth migration capture.